A chef is going to use a mixture of two brands of Italian dressing. The first brand contains 6% vinegar, and the second brand contains 11% vinegar. The chef wants to make 200 milliliters of a dressing that is 9% vinegar. How much of each brand should she use?

The chef will use 120 milliliters of 11% vinegar, and 80 milliliters of 6% vinegar.

Step-by-step explanation:

Since a chef is going to use a mixture of two brands of Italian dressing, and the first brand contains 6% vinegar, and the second brand contains 11% vinegar, and the chef wants to make 200 milliliters of a dressing that is 9% vinegar, to determine how much of each brand should she use the following calculation must be performed:

100 x 0.11 + 0 x 0.06 = 11

90 x 0.11 + 10 x 0.06 = 10.5

80 x 0.11 + 20 x 0.06 = 10

70 x 0.11 + 30 x 0.06 = 9.5

60 x 0.11 + 40 x 0.06 = 9

200 x 0.6 = 120

200 x 0.4 = 80

Thus, the chef will use 120 milliliters of 11% vinegar, and 80 milliliters of 6% vinegar.

solution:

the given function is ,

      =

the three roots of this quadratic function is , 0 ,8 and 10.all the roots are real and rational.

if a quadratic equation is of the form ,

sum of the roots = a + b +c= 0+8+10=18=  

product of roots taken two at a time = a b + b c+ c a = 0+80+0=80 =  

product of roots = a b c = 0=  

there are 11 doors in a hall starting from 0 to 11.the entry in the hall is permitted through gate number 0 and exit is allowed through only gate number 8 and 10.so, three roots(0,8,10) of quadratic function is given by entry and exit route of this hall.

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4